Calculate the mean, variance, and standard deviation. Show your solution. 1. X P(X) 1 0.11 2 0.49 3 0.33 4 0.07 2. X P(X) 2 2/10 4 3/10 6 4/10 8 1/10 3. X P(X) 1 0.25 3 0.13 4 0.35 6 0.27

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1.We find the mean as below

mean = ( (1*0.11) + (2*0.49) +(3*0.33) + (4*0.07) ) = 2.36

we define the variance as below

variance =( (12* 0.11) + (22 * 0.49) + (32 *0.33) + (42*0.07) ) - (mean)2

= (6.16 - 5.5696 ) = 0.5904

standard deviation = (variance)1/2 = (0.5904)1/2 = 0.768374908

2.We define the mean as below

mean = ( (2 * 2/10) + (4 * 3/10) + (6 * 4/10) + (8 * 1/10) ) = 4.8

we define the variance as below

variance = ( (22* 2/10) + (42 * 3/10) + (62 * 4/10) + (82 * 1/10) ) - (mean)2

= (26.4 - 23.04) = 3.36

standard deviation = (variance)1/2 = (3.36)1/2 = 1.833030278

3.We define the mean as below

mean = ( (1* 0.25) + (3* 0.13) + (4 * 0.35) + (6 * 0.27) ) = 3.66

we define the variance as below

variance = ( (12 * 0.25) + ( 32 * 0.13) + (42 * 0.35) + (62 * 0.27) ) - (mean)2

=(16.74 - 13.3956) = 3.3444

standard deviation = (variance)1/2 = (3.3444)1/2 = 1.828770078